Oversampling methods are known in the art of A/D and D/A conversion for overcoming problems associated with the use of analogue low-pass filters in conventional pulse code modulation. More particularly, in conventional systems, low-pass filters must be used to limit aliasing noise in A/D conversion and to smooth the output analogue signal in D/A conversion. However, VLSI does not lend itself well to the fabrication of high-precision analogue circuits.
Recent advances in oversampling techniques are discussed in a paper entitled Oversampling Methods for A/D and D/A Conversion by James C. Candy and Gabor C. Temes. Candy and Temes discuss a number of embodiments of Sigma-Delta modulators for oversampling conversion. One problem discussed by Candy and Temes is the provision of a feedback D/A converter in multi-bit Sigma-Delta converters. Specifically, the conversion error in the feedback D/A converter must be very small (i.e. less than half the least significant bit of the final output digital word). This is because any D/A conversion error which is added to the D/A output signal is directly subtracted from the input signal to the Sigma-Delta converter so as to appear in the digital output of the converter. Candy and Temes discuss a number of strategies for overcoming the problem of D/A error in Delta-Sigma modulators, such as trimming of D/A converter elements, randomization of errors introduced by mismatching of components, and digital correction of the D/A conversion error.
However, the prior art approach of trimming components has been found to be extremely expensive, and the use of digital error correction results in a requirement for extra correction hardware, as described in R. H. Walden, Catultepe, G. C. Temes, "Architectures for high-order multibit .SIGMA.-.DELTA. modulators," Proceedings of the 1990 IEEE International Symposium On Circuits and Systems, pp. 895-898 (May, 1990). The use of random averaging is known to result in a reduced signal-to-noise ratio (SNR) because all the harmonic distortions have been translated into white noise that falls partly inside the passband, as described in R. Carley, "A Noise-Shaping Coder Topology for 15+ Bit Converters," IEEE Journal of Solid-State Circuits, pp. 267-273 (April, 1989). Straightforward application of clocked averaging results in tones falling inside the passband, as well as an increase in passband noise, as discussed in greater detail below and as discussed in Yashui Sakina, P. Gray, "Multi-bit .SIGMA.-.DELTA. analog to digital converters with nonlinearity correction using dynamic barrel shifting," Master Thesis, pp. 24-32 (June 1990) & B. Leung, "Architectures for Multi-bit Oversampling A/D Converter Employing Dynamic Element Matching Techniques," 1991 IEEE International Symposium on Circuits and Systems, pp. 1657-1660 (May, 1991).